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Approximation Strategies for Incomplete MaxSAT

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Principles and Practice of Constraint Programming (CP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11008))

Abstract

Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of the unsatisfied soft clauses without providing any optimality guarantees. In this paper, we propose two approximation strategies for improving incomplete MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. Experimental results show that approximation strategies can be used to find better solutions than the best incomplete solvers in the MaxSAT Evaluation 2017.

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Notes

  1. 1.

    For simplicity, we will assume that \(\varphi _h\) is always satisfiable.

  2. 2.

    \(best(\varphi )\) is the cost of the best solution found by any solver in this evaluation.

  3. 3.

    We consider a score of 0 if \(\mathcal S\) did not find any solution to \(\varphi \).

  4. 4.

    Even though MaxHS [11] placed first in the complete weighted category of the MSE2017, its incomplete version is not as competitive as the other solvers [2].

References

  1. Alviano, M., Dodaro, C., Ricca, F.: A MaxSAT algorithm using cardinality constraints of bounded size. In: Proceedings of International Joint Conference on Artificial Intelligence, pp. 2677–2683. AAAI Press (2015)

    Google Scholar 

  2. Ansótegui, C., Bacchus, F., Järvisalo, M., Martins, R.: MaxSAT Evaluation 2017 (2017). http://mse17.cs.helsinki.fi/. Accessed 18 Apr 2017

  3. Ansótegui, C., Bonet, M.L., Gabàs, J., Levy, J.: Improving SAT-based weighted MaxSAT solvers. In: Milano, M. (ed.) CP 2012. LNCS, pp. 86–101. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33558-7_9

    Chapter  Google Scholar 

  4. Ansótegui, C., Gabàs, J.: WPM3: an (in)complete algorithm for weighted partial MaxSAT. Artif. Intell. 250, 37–57 (2017)

    Article  MathSciNet  Google Scholar 

  5. Argelich, J., Le Berre, D., Lynce, I., Marques-Silva, J., Rapicault, P.: Solving linux upgradeability problems using Boolean optimization. In: Proceedings of Workshop on Logics for Component Configuration, pp. 11–22. EPTCS (2010)

    Google Scholar 

  6. Argelich, J., Li, C.M., Manyà, F., Planes, J.: MaxSAT Evaluation 2016 (2016). http://maxsat.ia.udl.cat/. Accessed 18 Apr 2016

  7. Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Proceedings of International Joint Conference on Artificial Intelligence, pp. 399–404. AAAI Press (2009)

    Google Scholar 

  8. Le Berre, D., Parrain, A.: The SAT4J library, release 2.2. JSAT 7(2–3), 59–64 (2010)

    Google Scholar 

  9. Cai, S., Luo, C., Thornton, J., Su, K.: Tailoring local search for partial MaxSat. In: Proceedings of AAAI Conference on Artificial Intelligence, pp. 2623–2629. AAAI Press (2014)

    Google Scholar 

  10. Cai, S., Luo, C., Zhang, H., From decimation to local search and back: a new approach to MaxSAT. In: Proceedings of AAAI Conference on Artificial Intelligence, pp. 571–577. AAAI Press (2017)

    Google Scholar 

  11. Davies, J., Bacchus, F.: Solving MAXSAT by solving a sequence of simpler SAT instances. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 225–239. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23786-7_19

    Chapter  Google Scholar 

  12. Eén, N., Sörensson, N.: Translating pseudo-Boolean constraints into SAT. JSAT 2(1–4), 1–26 (2006)

    MATH  Google Scholar 

  13. Fan, Y., Ma, Z., Kaile, S., Sattar, A., Li, C.: Ramp: a local search solver based on make-positive variables. In: Proceedings of MaxSAT Evaluation (2016)

    Google Scholar 

  14. Feng, Y., Bastani, O., Martins, R., Dillig, I., Anand, S.: Automated synthesis of semantic malware signatures using maximum satisfiability. In: Proceedings of Network and Distributed System Security Symposium (2017)

    Google Scholar 

  15. Johnson, S.C.: Hierarchical clustering schemes. Psychometrika 32(3), 241–254 (1967)

    Article  Google Scholar 

  16. Jose, M., Majumdar, R.: Cause clue clauses: error localization using maximum satisfiability. In: Proceedings of Conference on Programming Language Design and Implementation, pp. 437–446. ACM (2011)

    Google Scholar 

  17. Joshi, S., Martins, R., Manquinho, V.: Generalized totalizer encoding for pseudo-Boolean constraints. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 200–209. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23219-5_15

    Chapter  Google Scholar 

  18. Koshimura, M., Zhang, T., Fujita, H., Hasegawa, R.: QMaxSAT: a partial Max-SAT solver. JSAT 8(1/2), 95–100 (2012)

    MathSciNet  MATH  Google Scholar 

  19. Luo, C., Cai, S., Kaile, S., Huang, W.: CCEHC: an efficient local search algorithm for weighted partial maximum satisfiability. Artif. Intell. 243, 26–44 (2017)

    Article  MathSciNet  Google Scholar 

  20. Luo, C., Cai, S., Wei, W., Jie, Z., Kaile, S.: CCLS: an efficient local search algorithm for weighted maximum satisfiability. IEEE Trans. Comput. 64(7), 1830–1843 (2015)

    Article  MathSciNet  Google Scholar 

  21. Marques-Silva, J., Argelich, J., Graça, A., Lynce, I.: Boolean lexicographic optimization: algorithms & applications. Ann. Math. Artif. Intell. 62(3–4), 317–343 (2011)

    Article  MathSciNet  Google Scholar 

  22. Martins, R., Joshi, S., Manquinho, V., Lynce, I.: Incremental Cardinality Constraints for MaxSAT. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 531–548. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10428-7_39

    Chapter  Google Scholar 

  23. Martins, R., Manquinho, V., Lynce, I.: Open-WBO: a modular MaxSAT solver’. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 438–445. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_33

    Chapter  Google Scholar 

  24. Morgado, A., Dodaro, C., Marques-Silva, J.: Core-guided MaxSAT with soft cardinality constraints. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 564–573. Springer, Cham (2014)

    Google Scholar 

  25. Saikko, P., Berg, J., Järvisalo, M.: LMHS: a SAT-IP hybrid MaxSAT solver. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 539–546. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_34

    Chapter  MATH  Google Scholar 

  26. Sugawara, T.: MaxRoster: solver description. In: Proceedings MaxSAT Evaluation 2017: Solver and Benchmark Descriptions, vol. B-2017-2, p. 12. University of Helsinki, Department of Computer Science (2017)

    Google Scholar 

  27. Warners, J.P.: A linear-time transformation of linear inequalities into conjunctive normal form. Inf. Process. Lett. 68(2), 63–69 (1998)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work is partially funded by ECR 2017 grant from SERB, DST, India, NSF award #1762363 and CMU/AIR/0022/2017 grant. Authors would like to thank the anonymous reviewers for their helpful comments, and Saketha Nath for lending his servers for the experiments.

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Authors and Affiliations

  1. Indian Institute of Technology Hyderabad, Sangareddy, India

    Saurabh Joshi, Prateek Kumar & Sukrut Rao

  2. Carnegie Mellon University, Pittsburgh, USA

    Ruben Martins

Authors
  1. Saurabh Joshi
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  2. Prateek Kumar
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  3. Ruben Martins
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  4. Sukrut Rao
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Corresponding author

Correspondence to Saurabh Joshi .

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Editors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    John Hooker

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Joshi, S., Kumar, P., Martins, R., Rao, S. (2018). Approximation Strategies for Incomplete MaxSAT. In: Hooker, J. (eds) Principles and Practice of Constraint Programming. CP 2018. Lecture Notes in Computer Science(), vol 11008. Springer, Cham. https://doi.org/10.1007/978-3-319-98334-9_15

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  • DOI: https://doi.org/10.1007/978-3-319-98334-9_15

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